Vortex Speckles with Customized Symmetry and Spatial Correlations

Abstract

A family of optical speckles with propagation-invariant annular morphology are generated via a phase-only mask and free-space evolution, termed vortex speckles, for which phase design is inspired by the vortex beam's helical wave front carrying orbital angular momentum. Vortex beams' graceful symmetry (central and/or axial) can be naturally inherited into vortex speckles by adjusting the parity of the topological value $\ensuremath{\ell}$ and the consistency of the initial phase angle ${\ensuremath{\phi}}_{0}$. By sequentially imprinting such a series of phase profiles onto a spatial light modulator, the resultant stochastically fluctuating vortex speckles naturally constitute an annular pseudothermal light field, and the customized symmetry in intensity profiles leads to spatial correlations, which are exploited for Hanbury Brown and Twiss interferometry and beam-splitter-free lensless ghost imaging and diffraction experiments. Symmetric annular pseudothermal light also has diverse phase correlations, so in a proposed vortex self-interferometer, we can manipulate photon correlations (parity-induced anticorrelation) and observe intriguing correlation states (spatially varying photon correlation oscillations). This work not only presents a flexible light-source option for applications requiring ring-shaped speckle illumination, but it also paves the way for the customization of nontrivial classical correlation modes.